Jack M. Guttentag The Mortgage Professor

Few borrowers understand exactly how mortgages amortize, and some professionals don't either. I recently exchanged emails with a financial planner who was proposing a novel method of saving interest on a mortgage. His method didn't work because it was predicated on an erroneous assumption about how loans amortize.

While mortgage amortization accounting is not the easiest thing in the world to understand, it isn't rocket science either. Since borrowers are stuck with their mortgages for years, and the firms that record the changing status of their loans sometimes make mistakes, it is a good idea to know how the accounting works.

Except for simple-interest mortgages, the accounting for amortized home loans assumes that there are only 12 days in a year, consisting of the first day of each month. Your account begins on the first day of the month following the day your loan closes. You pay "interim interest" for the period between the closing day and the day your record begins. Your first monthly payment is due on the first day of the month after that.

For example, if your 6 percent 30-year $100,000 loan closes on March 15, you pay interest at closing for the period of March 15 to April 1, and your first payment of $599.56 is due May 1.

The payment is allocated between interest and reduction in the loan balance, which is called principal. The interest payment is calculated by multiplying 1/12 of the interest rate times the loan balance in the previous month. 1/12 of .06 is .005. The interest due May 1, therefore, is .005 times $100,000, or $500. The remaining $99.56 is principal, and it reduces the balance to $99,900.44.
The principal payment is always a residual -- the difference between the total payment and the interest due.

The process repeats each month, but the portion of the payment allocated to interest gradually declines while the portion allocated to principal gradually rises. On June 1, the interest due is .005 times $99,900.44, or $499.51. The amount available for principal rises to $100.06.

While the payment is due on the first day of each month, lenders allow borrowers a grace period, which is usually 15 days. A payment received on the 15th is treated exactly in the same way as a payment received on the 1st. A payment received after the 15th, however, is assessed a late charge equal to 4 or 5 percent of the payment.

When borrowers elect to increase the amount of their payment, the principal payment increases by the same amount, so the balance is reduced by that amount. For example, if the borrower paid $699.56 on May 1, the balance would drop by an additional $100 to $99,700.38, which in turn would reduce the interest due in June to $498.51.

Extra payments that are made later in the month might have the same effect, or might not be credited until the following month, depending on the lender. To be credited within the same month, extra payments have to be received before the Nth day of the month, but N varies from one lender to another.

These rules are advantageous to many, perhaps to most borrowers because of the backdating of payments to the first day of the month. Thus, the borrower who pays $599.56 on May 15 has the use of $599.56 free of interest for 15 days. The same is true of extra payments received before the Nth day of the month.

Mortgage Amortization Tools

Readers are encouraged to develop an actual amortization schedule that will allow them to see exactly how the numbers change. They can do that using one of my calculators. For straight amortization without extra payments, use my calculator 8a.  To see how amortization is impacted by extra payments, use 2a. To experiment with different payments and/or maintain a permanent record of your loan, download one of my spreadsheets, Extra Payments on Monthly Payment Fixed-Rate Mortgages or Extra Payments on ARMs (adjustable-rate mortgages). Unlike the calculators which can't be moved from where they are, the spreadsheets can be transferred to the hard drive of your computer.